(A) Find the position of a particle on a circle of radius R with center at the origin. Assume that theta is the angle of the position vector with the axis. Express your answer in terms of the variables R, and Theta , and unit vectors i hat, and j hat .
(B) If the particle moves with constant speed v starting on the x-axis at t = 0, find an expression for in terms of time t and the period T to complete a full circle. Express your answer in terms of the variables t, T, and appropriate constants.
(C) Differentiate the position vector twice with respect to time to find the acceleration, and find its magnitude.